Im a bit unsure and have to get advice.
I have the:

public class MyApp extends JFrame{

And from there i do;

MyServer = new MyServer (this);
MyServer.execute();

MyServer is a:

public class MyServer extends SwingWorker<String, Object> {   

MyServer is doing listen_socket.accept() in the doInBackground()

and on connection it create a new

class Connection implements Runnable {

I have the belove DbHelper that are a singleton.

It holds an Sqlite connected. Im initiating it in the above MyApp
and passing references all the way in to my runnable:

class Connection implements Runnable {

My question is what will happen if there are two simultaneous read or `write?
My thought here was the all methods in the singleton are synchronized and
would put all calls in the queue waiting to get a lock on the synchronized method.

Will this work or what can i change?

public final class DbHelper {

    private boolean initalized = false;
    private String HomePath = "";
    private File DBFile;

    private static final String SYSTEM_TABLE = "systemtable";   
    Connection con = null;
    private Statement stmt;
    private static final ContentProviderHelper instance = new ContentProviderHelper ();

    public static ContentProviderHelper  getInstance() {

        return instance;

    }

    private DbHelper () {

        if (!initalized)
        {
            initDB();

            initalized = true;
        }
    }

    private void initDB()
    {
        DBFile = locateDBFile();
        try {

            Class.forName("org.sqlite.JDBC");

            // create a database connection
            con = DriverManager.getConnection("jdbc:sqlite:J:/workspace/workComputer/user_ptpp");

        } catch (SQLException e) {
            e.printStackTrace();
        } catch (ClassNotFoundException e) {
            e.printStackTrace();
        }
    }

    private File locateDBFile()
    {
        File f = null;
        try{
            HomePath = System.getProperty("user.dir");
            System.out.println("HomePath: " + HomePath);
            f = new File(HomePath + "/user_ptpp");
            if (f.canRead())
                return f;
            else
            {
                boolean success = f.createNewFile();
                if (success) {
                    System.out.println("File did not exist and was created " + HomePath);
                    // File did not exist and was created
                } else {
                    System.out.println("File already exists " + HomePath);

                    // File already exists

                }
            }
        } catch (IOException e) {
             System.out.println("Maybe try a new directory. " + HomePath);
            //Maybe try a new directory.
        }
        return f;
    }

    public String getHomePath()
    {
        return HomePath;
    }

    private synchronized String getDate(){

        SimpleDateFormat dateFormat = new SimpleDateFormat("yyyy-MM-dd HH:mm:ss"); 
        Date date = new Date();
        return dateFormat.format(date);
    }


    public synchronized String getSelectedSystemTableColumn( String column) {

        String query = "select "+ column + " from " + SYSTEM_TABLE ;
        try {
            stmt = con.createStatement(ResultSet.TYPE_FORWARD_ONLY, ResultSet.CONCUR_READ_ONLY);
            ResultSet rs = stmt.executeQuery(query);
            while (rs.next()) {

                String value = rs.getString(column);

                if(value == null || value == "")
                    return "";
                else
                    return value;
            }

        } catch (SQLException e ) {
            e.printStackTrace();
            return "";
        } finally {

        }
        return "";

    }

}